That would indeed be pretty cool.
According to my knowledge of signal processing, psychoacoustics and digital logic, it can not possible affect the sound quality in any audible way.
At worst it will create a noise of amplitude 1 LSB, that is -96dB full scale. This is not audible. And in reality the noise will be even lower. You'd need to lower the volume this way a couple thousand times to even hope to get an audible result.